Edit: Whoops, misread the question. You may want to just read the wikipedia page on fractals, skip the first section and read Introduction. Basically they're shapes with simple mathematical definitions that have an extremely high degree of complexity. As you zoom in, they still exhibit complexity, and repeat the same sorts of shapes as the zoomed-out versions.

Hurry up and make some adjustable parameters for this script before someone else does! You've got something really potentially bitchen here, Kai's Power Tools for Minecraft. If I had time I'd be on this already, JFTR.

Think of the sick things you could make with a robust set of fractal filters... oh my god.

It gets a lot more complex then this, but fractals are often what is called "self-similar", so if you zoom in on any part of it you will see the whole fractal, just smaller. A popular example is the Sierpinski triangle. If you notice, looking at any part of it will show you a smaller Sierpinski triangle, repeated to infinity. The Mandlebrot set, which Sethbling showed, actually deals which imaginary numbers and the complex plane, but I don't know as much about that.

Meh, I got a much better feel for the mandelbulb out of Minecraft than I did from the image. Any rendering system is going to be rough, and you could use the same script to zoom in on the mandelbulb too.

I once wrote a program in C++ to do ASCII art of the mandelbrot set, but I lost it when back when my hard drive gave out on me. I reimplemented the math part in Common Lisp in 6 lines. (It has built in complex numbers!) Not sure what happened to that, though. Next time I do a programming project, I'm definitely throwing it up on github where it'll be safe.